Constructing and analyzing of a unique three-dimensional chaotic autonomous system exhibiting three families of hidden attractors

A three-dimensional chaotic autonomous system is proposed in this paper. This system has a unique property: it can belong to three different families of chaotic systems with hidden attractors: (a) systems with a line of equilibria, (b) systems with only stable equilibria, and (c) systems with no equilibria. Dynamics of this system are investigated through eigenvalue structures, phase portraits, basin of attraction, bifurcation diagram and Lyapunov exponents. The physical existence of the chaotic behavior found in the proposed system is verified by using OrCAD-PSpice software. A good qualitative agreement is shown between the simulations and the PSpice results.